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A potentiometer wire of length 100 cm ha...

A potentiometer wire of length 100 cm has a resistance of `100Omega` it is connected in series with a resistance and a battery of emf 2 V and of negligible internal resistance. A source of emf 10 mV is balanced against a length of 40 cm of the potentiometer wire. what is the value of the external resistance?

Text Solution

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As shown in the figure, if R is the unknown resistance, the current in the circuit
`I=(V)/(r+R)=(2)/(10+R)`
Now, as the 100 cm wire has a resistance of `10Omega`, the resistance of 40 cm of wire will be `40 xx (10//100) = 4 ohm`. Potential drop across 40 cm wire will be` V = I xx 4` But, here `V = 10 mV `(given)
`i=(2)/((10+R))=(1)/(400),i.e.R=790Omega`
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